1. Two ways to get a column of another column with max/min values:

　　a. most_bars_country = flags["name"][flags["bars"].idxmax()]

　　b. bars_sorted = flags.sort_values("bars", ascending=[0])

　　　　most_bars_country = bars_sorted["name"].iloc[0]

2. The way to get the probability of a certain value in a column:

　　orange_probability = flags[flags["orange"]==1].shape[0]/flags.shape[0]

3. The way to calculate combination by using factorial：　

　　import math
　　def find_outcome_combinations(N, k): # Calculate the numerator of our formula.
　　　　numerator = math.factorial(N) # Calculate the denominator.
　　　　denominator = math.factorial(k) * math.factorial(N - k) # Divide them to get the final value.
　　　　return numerator / denominator

4. 

Statistics and Linear Algebra 6